Errors in machines and mechanisms such as gear pairs and trains, leading screw pairs, racks and pinions, etc. may be caused by continuous deviations of a driven member from its theoretically correct positions. In other words, the actual position of the driven member may not correspond to the theoretical position of the driven member which is powered by a driving member. Such errors may constitute the main source of vibrations and noise in machines, a loss of efficiency and may lead to other hazardous consequences that should be avoided. In order to improve a machine's design and production, it may be necessary to examine its kinematic accuracy or error to determine which elements of the machine are defective. In gear pairs for example, kinematic accuracy or error may range from ArcSeconds to hundreds of ArcSeconds. Such small deviations are very difficult to determine with accuracy, and devices for checking kinematic accuracy or error are generally incapable of measuring such small deviations because of their lack of precision. Until the beginning of the 1960's, the angle measurements of kinematic accuracy or error were typically performed by optical geodesic devices. Geodesic devices, however, have only limited resolution.
Incremental encoders are now typically used as an alternative to manual manipulated optic-geodesic devices for measuring kinematic accuracy or error in machines and mechanisms. One incremental encoder is typically mounted on a driving element while another is mounted on a driven element. The outputs of both incremental encoders are connected to a phase meter through proper frequency dividers. The incremental encoders operate by fractioning measuring coordinates on multiple index intervals on a uniform scale or raster, such as, for example, an optical, magnetic, mechanical or any other angular scale, attached to the driving and driven elements of a machine or mechanism. A principle on which the prior incremental measurement method is based, is fractioning of measuring coordinates on multiple index intervals in the form of a uniform raster-type scale.
One problem with incremental measurement is the elimination of background carrying signal that is generated by the grades or intervals. In the beginning of every measurement cycle, the deviation between the actual position and theoretical position of a rotary member is negligible. At the beginning of this measurement cycle, any such deviation represents the kinematic accuracy or error. At the next measurement cycle, the deviation will be transferred to the next interval. By using incremental encoders to obtain a discrete representation of the rotation of a gear, the discrete seria in the form of a periodic function may be transformed in the continuous form by integration. Measurement of the phase difference between two discrete signals received from two incremental encoders, which are attached to the driving and driven members (elements) of a machine or mechanism and balanced to the same frequency by frequency dividers, may then be obtained.
The degree of approximation will depend on the number of indexes that are involved in the measurements. The greater the number of intervals the better the approximation to the real function of kinematic accuracy or error. The number of grades of the scale (or the number of pulses on the output of the interface-interpolator) has only technological performance limits. The transfer of the deviation in a rotary member's position for a previous cycle to a subsequent cycle requires the encoder to run constantly. The measurement of kinematic accuracy or error for multiple rotation cycles will be impossible if a machine is not running because the continuous process of coordinate transference will be interrupted and accumulated information will be lost. For this reason, accurate measurement of quasi static or static parameters of accuracy is impossible for devices based using frequency dividers and phasemeter-traditional measuring schemes incorporating incremental encoders. Another problem associated with using incremental encoders to measure kinematic accuracy or error is the level of approximation of a real function of kinematic accuracy or error by its discrete image. According to information theory, this approximation is different for each harmonic component. Therefore, due to the limited number of encoder grades or intervals, upper harmonic components of kinematic accuracy or error may represent a very small amount of the measurement. Also, the level of accuracy of measurements for upper harmonics is not the same as for lower harmonics.
Another disadvantage of the incremental encoder method relates to the necessary adjustment of the ratio of controlled gears of a machine or mechanism. A phase meter measures only when the frequency of both canals is the same. When the incremental encoders utilize the same increment spacing and the measured gears do not, a common scale for each incremental encoder must be obtained and each encoder should be connected with its own frequency divider to obtain a complete balance of frequencies. However, even using frequency dividers some measuring information would be inevitably lost, thereby negatively affecting the resolution capability of the device. Moreover, in some instances it is impossible to establish a correct ratio between incremental encoders because the intervals on each encoder are not divisible by a common denominator and therefore a common scale cannot be found. The same difficulties would be obtained if a combination of both dividers and multipliers were used to manage the same balance problem of frequencies.